Axisymmetric interaction of an acoustic wave with a thin elastic spherical shell stiffened by an elastic rib

In nonstationary formulation in the context of the classical theories of shells and curvilinear rods we solve the axisymmetric problem of scattering of sound on a spherical shell stiffened by a rib. We analyze the effect of the rib on the spectral density of the echo-signal. We give the results of computing the reflected pulse and classify the sequence of pulses of peripheral waves in the echo-signal. Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 2, 1997, pp. 142–147.     

Parametric oscillations of an orthotropic cylindrical shell with an elastic filler I. Formulation of the problem

A linear model of a Timoshenko-type shell with an elastic filler is proposed for solving the problem of the parametric oscillations of the system. A class of operators is derived, which act in a Hilbert space, for which the problem of the determination of a spectrum of eigen-values permits an iterative scheme of solution. Thus, the method for solving problems of parametric oscillations of structures proposed by Bolotin is confirmed.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 470–478, May–June, 1974.     

Effect of transverse shear on the stability of an orthotropic cylindrical shell with an elastic core in axial compression

The effect of transverse shear on the stability of a composite shell in axial compression has been investigated. The core is treated as an isotropic elastic cylinder bonded to the inner surface of the shell. The effect of the tangential shearing forces between the shell and the core is taken into account.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 267–273, March–April, 1973.     

Torsional stability of a glass-reinforced plastic cylindrical shell with an elastic core

The problem of the stability of a glass-reinforced plastic cylindrical shell with an elastic core subjected to twisting moments applied to the edges of the shell is considered. As in various other studies [4–6], the glass-reinforced plastic is treated as an elastically orthotropic material. The core is treated as an isotropic elastic cylinder, whose outer surface is bonded to the shell. Expressions for the critical stresses are obtained for an infinitely long shell and a shell of finite length.Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 1082–1086, November–December, 1970.     

Structural damping in an equi-strength cylindrical shell with an elastic filler

We present a method for rational application of the deformation properties of a shell system with an elastic filler: design of a shell with variable thickness while preserving the load-bearing ability of the system as a whole. For the equi-strength shell thereby obtained we state and solve the mixed contact problem taking account of dry friction with nonmonotone loading, making it possible to estimate the structural hysteresis in the system. Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 37, 1994, pp. 86–91.     

Dual problem of optimizing an orthotropic cylindrical shell

The problem of optimizing the weight of an orthotropic cylindrical shell is examined, using the duality theory of geometrical programing.     

Bulging of a cylindrical shell with viscoelastic filler during axial compression

The problem of static stability during axial compression of an orthotropic cylindrical shell reinforced by a continuous filler is solved. The filler is considered to be a three-dimensional isotropic linear-viscoelastic body, fixed at its outer surface to the shell. Transverse shear in the shell is taken into account. The loss of stability of the structure is related to the time-dependent development of initial defects, following application of a load, which is smaller than the instant critical load.     

Bending of a multilayer cylindrical shell with an elastic core under a local radial load

The problem of the state of stress and strain of a multilayer cylindrical shell with a soft elastic core subjected to an external, locally distributed radial load is solved under the simplifying assumption that all the layers satisfy the generalized Hooke's law and work together without slip. A numerical example is given.     

Residual stresses in a closed cylindrical shell with a longitudinal crack

We study the influence of the residual stresses on the size and character of the variations in the strain intensity and moment intensity coefficients in a closed cylindrical shell welded together from two parts and under the action of axisymmetric loads. We perform a numerical analysis in the case when the shell with residual stresses is acted on by internal pressure.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 27, 1988, pp. 40–45.     

Study of oscillations in a viscoelastic cylindrical shell in an elastic medium

An equation was obtained and solved for oscillations in a viscoelastic cylindrical shell located in the ground. A numerical example is examined.Moscow Electronic Engineering Institute. Translated from Mekhanika Polimerov, No. 1, pp. 178–181, January–February, 1974.     

Stability with the axial compression of an axisymmetrically heated orthotropic cylindrical shell fastened to an elastic cylinder which is pliable with respect to shear

The article gives a solution to the problem of stability with the axial compression of an axisymmetrically heated orthotropic cylindrical shell fastened to an elastic thin-walled cylinder through an intermediate layer. It is assumed that the parameters of the elasticity of the orthotropic shell depend on the temperature, and vary over the thickness of the wall. The intermediate layer is assumed to be isotropic and absolutely rigid in a radial direction, but pliable with respect to axial shear. The thin-walled cylinder is considered to be elastic, isotropic, and unheated.Scientific-Research Institute for Chemical Engineering, Moscow Region. Translated from Mekhanika Polimerov, No. 3, pp. 546–550, May–June, 1970.     

Optimization of a cylindrical composite shell with a viscoelastic core in axial compression

The problem of the optimal design of a composite shell in creep is formulated. The progressive buckling of a cross-wound reinforced cylindrical shell supported on a viscoelastic core is considered as a particular case. The reinforcement structure and shell thickness corresponding to minimum weight for a given load and service life are found.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 442–446, May–June, 1975.     

Dynamic interaction of a thin cylindrical shell with a viscous liquid

Based on the principle of the possible displacements in an axially symmetric formulation, the dynamic interaction of a circular cylindrical shell with a viscous compressible liquid under nonstationary loading by a rectangular pulse is studied. The problem is solved using an orthonormal system of basis functions obtained by applying a Gramm-Schmidt algorithm to an initial nonorthogonal system of basis functions. Results from numerical studies are presented. Solutions using nonorthogonal and orthogonal systems of basis functions are compared.     

Dynamic stability of an elastic orthotropic cylindrical shell with allowance for transverse shears

The resolvents for the dynamic stability of an elastic orthotropic cylindrical shell are obtained in accordance with the Ambartsumyan and Timoshenko-type refined theories. The regions of instability given by the classical and refined theories are compared. The dependence of the refinements on the shell parameters, the shear moduli of the material, and the buckling modes are investigated.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 312–320, March–April, 1973.     

Stability of a transversely isotropic cylindrical shell in axial compression

The problem of the stability of a transversely isotropic cylindrical shell subjected to axial compression is considered with the aid of three-dimensional linearized equations for small subcritical strains. Transcendental equations are obtained for the critical loads corresponding to axisymmetric and nonaxisymmetric deformation. It is shown that in the case of the axisymmetric buckling mode the Kirchhoff-Love hypothesis is asymptotically exact irrespective of the properties of the material. The dependence of the critical load on the properties of the shell material is investigated numerically. Graphs of the variation of the critical load with relative shear modulus are presented.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 6, pp. 1064–1068, November–December, 1969.     

The response of a plastic cylindrical shell to axial impact

Zusammenfassung Es wird eine Theorie des plastischen Knichens zylindrischer Schalen unter axialer Stossbelastung aufgestellt und eine Formel angegeben für die Stossgeschwindigkeiten, weilche in einer gegebenen Schale kleine Biegewellen erzeugen. Ferner wird eine einfache Berechnungsmethode für die Eigenfunktionen der Biegeschwingungen angegeben. Die Übereinstimmung der Theorie mit Versuchsergebnissen ist gut.     

Dynamic stability of cylindrical orthotropic shells with an elastic core under a longitudinal periodic load

The dynamic instability of a cylindrical orthotropic shell with an elastic core subjected to a longitudinal periodic load is considered. Equations are obtained for determining the regions of dynamic instability for different core models.     

Electro-thermo-mechanical torsional buckling of a piezoelectric polymeric cylindrical shell reinforced by DWBNNTs with an elastic core

The effect of partially filled poly ethylene (PE) foam core on the behavior of torsional buckling of an isotropic, simply supported piezoelectric polymeric cylindrical shell made from polyvinylidene fluoride (PVDF), and subjected to combined electro-thermo-mechanical loads has been analyzed using energy method. The shell is reinforced by armchair double walled boron nitride nanotubes (DWBNNTs). The core is modeled as an elastic environment containing Winkler and Pasternak modules. Using representative volume element (RVE) based on micromechanical modeling, mechanical, electrical and thermal characteristics of the equivalent composite were determined. Critical buckling load is calculated using strains based on Donnell theory, the coupled electro-thermo-mechanical governing equations and principle of minimum potential energy. The results indicate that buckling strength increases substantially as harder foam cores are employed i.e. as E_c/E_s is increased. The most economic in-fill foam core is at η = 0.6, as cost increases without much significant improvement in torsional buckling at higher η’s.     

Stability of a layered cylindrical shell with a transversely isotropic core in axial compression

The problem of the stability of a cylindrical shell with a transversely isotropic core in axial compression is considered. A solution is obtained for the axisymmetric case.